We prove the generalized Ulam stability of ternary homomorphisms from commutative ternary semigroups into n-Banach spaces as well as into complete non-Archimedean normed spaces. Ternary algebraic structures appear in various domains of theoretical and mathematical physics, and p-adic numbers, which are the most important examples of non-Archimedean fields, have gained the interest of physicists...

in this paper, we consider a generalization of the real normed spaces and give some examples.

In this work, our purpose is to introduce I−convergence of sequences of functions in intuitionistic fuzzy normed space by combining the I−convergence, the sequences of functions and the intuitionistic fuzzy normed spaces, and to investigate relations among concepts such as I−convergence, statistical convergence and the usual convergence of sequences of functions in intuitionistic fuzzy normed s...

in this paper, we prove the generalized hyers-ulam(or hyers-ulam-rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real ...

we introduce some new concepts of topological spaces which say α − separable topologicalspace and o-topological group, α − first axiom, α − second axiom, and we find some relations betweenthem with some applications in normed spaces.

the goal of  this paper is to investigate the solutionand stability in random normed spaces, in non--archimedean spacesand also in $p$--banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.

We describe the computations of some intrinsic constants associated to an n-dimensional normed space V, namely the N -th “allometry” constants κ∞(V) := inf { ‖T‖ · ‖T ′‖, T : `∞ → V, T ′ : V → `∞, TT ′ = IdV } . These are related to Banach–Mazur distances and to several types of projection constants. We also present the results of our computations for some low-dimensional spaces such as sequenc...

In this paper, we prove that in a finite dimensional probabilistic normed space, every two probabilistic norms are equivalent and we study the notion of Dcompactness and D-boundedness in probabilistic normed spaces.